4 files changed, 87 insertions, 74 deletions
diff --git a/dissertation.tex b/dissertation.tex
index b1e219b..d8bf32a 100644
--- a/dissertation.tex
+++ b/dissertation.tex
@@ -89,6 +89,7 @@ This dissertation is approved by the following members of the Final Oral Committ
 %\include{procedures/chapter}
 %\include{hardware/chapter}
 % TODO: consider inserting WrightTools documentation as PDF
+\include{irf/chapter}
 %\include{errata/chapter}
 %\include{colophon/chapter}
 \end{appendix}
diff --git a/irf/chapter.tex b/irf/chapter.tex
new file mode 100644
index 0000000..07cd561
--- /dev/null
+++ b/irf/chapter.tex
@@ -0,0 +1,69 @@
+\chapter{Instrumental response function} \label{cha:irf}
+
+The instrumental response function (IRF) is a classic concept in analytical science.  %
+Defining IRF becomes complex with instruments as complex as these, but it is still useful to
+attempt.  %
+
+It is particularly useful to define bandwidth.
+
+\subsubsection{Time Domain}
+
+I will use four wave mixing to extract the time-domain pulse-width.   %
+I use a driven signal \textit{e.g.} near infrared carbon tetrachloride response.  %
+I'll homodyne-detect the output.  %
+In my experiment I'm moving pulse 1 against pulses 2 and 3 (which are coincident).  %
+
+The driven polarization, $P$, goes as the product of my input pulse \textit{intensities}:
+
+\begin{equation}
+P(T) = I_1(t-T) \times I_2(t) \times I_3(t)
+\end{equation}
+
+In our experiment we are convolving $I_1$ with $I_2 \times I_3$.  %
+Each pulse has an \textit{intensity-level} width, $\sigma_1$, $\sigma_2$, and $\sigma_3$. $I_2
+\times I_3$ is itself a Gaussian, and  
+\begin{eqnarray}
+\sigma_{I_2I_3} &=& \dots \\
+&=& \sqrt{\frac{\sigma_2^2\sigma_3^2}{\sigma_2^2 + \sigma_3^2}}.
+\end{eqnarray}
+
+The width of the polarization (across $T$) is therefore
+
+\begin{eqnarray}
+\sigma_P &=& \sqrt{\sigma_1^2 + \sigma_{I_2I_3}^2} \\
+&=& \dots \\ 
+&=& \sqrt{\frac{\sigma_1^2 + \sigma_2^2\sigma_3^2}{\sigma_1^2 + \sigma_2^2}}. \label{eq:generic}
+\end{eqnarray}
+
+% TODO: determine effect of intensity-level measurement here
+
+I assume that all of the pulses have the same width.   %
+$I_1$, $I_2$, and $I_3$ are identical Gaussian functions with FWHM $\sigma$. In this case,
+\autoref{eq:generic} simplifies to  
+
+\begin{eqnarray}
+\sigma_P &=& \sqrt{\frac{\sigma^2 + \sigma^2\sigma^2}{\sigma^2 + \sigma^2}} \\
+&=& \dots \\
+&=& \sigma \sqrt{\frac{3}{2}}
+\end{eqnarray}
+
+Finally, since we measure $\sigma_P$ and wish to extract $\sigma$:
+
+\begin{equation}
+\sigma = \sigma_P \sqrt{\frac{2}{3}}
+\end{equation}
+
+Again, all of these widths are on the \textit{intensity} level.
+
+\subsubsection{Frequency Domain}
+
+We can directly measure $\sigma$ (the width on the intensity-level) in the frequency domain using a
+spectrometer.  %
+A tune test contains this information.  %
+
+\subsubsection{Time-Bandwidth Product}
+
+For a Gaussian, approximately 0.441
+
+% TODO: find reference
+% TODO: number defined on INTENSITY level!
+\ No newline at end of file
diff --git a/spectroscopy/auto/chapter.el b/spectroscopy/auto/chapter.el
index f316ae6..b067440 100644
--- a/spectroscopy/auto/chapter.el
+++ b/spectroscopy/auto/chapter.el
@@ -7,7 +7,6 @@
     "spc:fig:trive_off_diagonal"
     "spc:fig:trive_population_transfer"
     "fig:ta_and_tr_setup"
-    "eq:ta_complete"
-    "eq:generic"))
+    "eq:ta_complete"))
  :latex)
 
diff --git a/spectroscopy/chapter.tex b/spectroscopy/chapter.tex
index 030edd5..2cf088b 100644
--- a/spectroscopy/chapter.tex
+++ b/spectroscopy/chapter.tex
@@ -145,10 +145,19 @@ WMEL diagrams are drawn using the following rules.  %
 	\item Output is represented as a solid wavy line.
 \end{denumerate}
 
+Representative WMELs can be found in Figures [xxxxxx].  %
+
 % TODO: representative WMEL?
 
 \section{Types of spectroscopy}  % ================================================================
 
+Scientists have come up with many ways of exploiting light-matter interaction for measurement
+purposes.  %
+This section discusses several of these strategies.  %
+I start broadly, by comparing and contrasting differences across categories of spectroscopies.  %
+I then go into relevant detail regarding a few experiments that are particularly relevant in this
+dissertation.  %
+
 \subsection{Linear vs multidimensional}  % --------------------------------------------------------
 
 This derivation adapted from \textit{Optical Processes in Semiconductors} by Jacques I. Pankove
@@ -170,6 +179,8 @@ To extend reflectivity to a differential measurement
 Nonlinear spectroscopy relies upon higher-order terms in the light-matter interaction. In a generic
 system, each term is roughly ten times smaller than the last.  % TODO: cite?
 
+TODO: Basic ``advantage of dimensionality'' figure.
+
 \subsection{Homodyne vs heterodyne}  % ------------------------------------------------------------
 
 Two kinds of spectroscopies: 1) heterodyne 2) homodyne.
@@ -182,6 +193,8 @@ This literally means that homodyne signals go as the square of heterodyne signal
 mean when we say that homodyne signals are intensity level and heterodyne signals are amplitude
 level.
 
+Homodyne dynamics go faster: cite Darien correction
+
 \subsection{Frequency vs time domain}  % ----------------------------------------------------------
 
 Time domain techniques become more and more difficult when large frequency bandwidths are
@@ -203,6 +216,8 @@ Since time-domain pulses in-fact possess all colors in them they cannot be trust
 perturbative fluence.  %
 See that paper that Natalia presented...  %
 
+See Paul's dissertation
+
 \subsection{Transient grating}  % -----------------------------------------------------------------
 
 Triply Electronically Enhanced (TrEE) spectroscopy has become the workhorse homodyne-detected 4WM
@@ -318,11 +333,10 @@ expression for $\Delta A$ that only depends on my eight measurables.  %
 \Delta A = - \log_{10} \left(\frac{C_\mathrm{T}(V_\mathrm{T} + V_{\Delta\mathrm{T}}) + C_\mathrm{R}(V_\mathrm{R} + V_{\Delta\mathrm{R}})}{C_\mathrm{T} V_\mathrm{T} + C_\mathrm{R} V_\mathrm{R}}\right)
 \end{equation}
 
-\subsection{Pump CMDS-probe}  % -------------------------------------------------------------------
-
 \clearpage
 \section{Instrumentation}  % ======================================================================
 
+In this section I introduce the key components of the MR-CMDS instrument.  %
 
 \subsection{LASER}  % -----------------------------------------------------------------------------
 
@@ -333,73 +347,3 @@ expression for $\Delta A$ that only depends on my eight measurables.  %
 \subsection{Delay stages}  % ----------------------------------------------------------------------
 
 \subsection{Spectrometers}  % ---------------------------------------------------------------------
-
-\subsection{Instrumental response function}  % ----------------------------------------------------
-
-The instrumental response function (IRF) is a classic concept in analytical science.  %
-Defining IRF becomes complex with instruments as complex as these, but it is still useful to
-attempt.  %
-
-It is particularly useful to define bandwidth.
- 
-\subsubsection{Time Domain}
-
-I will use four wave mixing to extract the time-domain pulse-width.   %
-I use a driven signal \textit{e.g.} near infrared carbon tetrachloride response.  %
-I'll homodyne-detect the output.  %
-In my experiment I'm moving pulse 1 against pulses 2 and 3 (which are coincident).  %
-
-The driven polarization, $P$, goes as the product of my input pulse \textit{intensities}:
-
-\begin{equation}
-P(T) = I_1(t-T) \times I_2(t) \times I_3(t)
-\end{equation}
-
-In our experiment we are convolving $I_1$ with $I_2 \times I_3$.  %
-Each pulse has an \textit{intensity-level} width, $\sigma_1$, $\sigma_2$, and $\sigma_3$. $I_2
-\times I_3$ is itself a Gaussian, and  
-\begin{eqnarray}
-\sigma_{I_2I_3} &=& \dots \\
-&=& \sqrt{\frac{\sigma_2^2\sigma_3^2}{\sigma_2^2 + \sigma_3^2}}.
-\end{eqnarray}
-
-The width of the polarization (across $T$) is therefore
-
-\begin{eqnarray}
-\sigma_P &=& \sqrt{\sigma_1^2 + \sigma_{I_2I_3}^2} \\
-&=& \dots \\ 
-&=& \sqrt{\frac{\sigma_1^2 + \sigma_2^2\sigma_3^2}{\sigma_1^2 + \sigma_2^2}}. \label{eq:generic}
-\end{eqnarray}
-
-% TODO: determine effect of intensity-level measurement here
-
-I assume that all of the pulses have the same width.   %
-$I_1$, $I_2$, and $I_3$ are identical Gaussian functions with FWHM $\sigma$. In this case,
-\autoref{eq:generic} simplifies to  
-
-\begin{eqnarray}
-\sigma_P &=& \sqrt{\frac{\sigma^2 + \sigma^2\sigma^2}{\sigma^2 + \sigma^2}} \\
-&=& \dots \\
-&=& \sigma \sqrt{\frac{3}{2}}
-\end{eqnarray}
-
-Finally, since we measure $\sigma_P$ and wish to extract $\sigma$:
-
-\begin{equation}
-\sigma = \sigma_P \sqrt{\frac{2}{3}}
-\end{equation}
-
-Again, all of these widths are on the \textit{intensity} level.
-
-\subsubsection{Frequency Domain}
-
-We can directly measure $\sigma$ (the width on the intensity-level) in the frequency domain using a
-spectrometer.  %
-A tune test contains this information.  %
-
-\subsubsection{Time-Bandwidth Product}
-
-For a Gaussian, approximately 0.441
-
-% TODO: find reference
-% TODO: number defined on INTENSITY level!
-\ No newline at end of file